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Hotelling (1929) - Stability In Competition (view source)
Revision as of 16:04, 19 June 2010
, 16:04, 19 June 2010→Ernesto Dal Bo's Model
*<math>mc=0\,</math>
*unit demands
*consumers are homogeneous with valuation <math>v \,</math> (assumed large enough to cover the market)
*there are transportation costs
:<math>p_1 + t(x-a)^2 = p_2 +t(1-b-x)^2 \,</math>
Rearranging for <math>x \,</math> gives us the demand function for <math>q_1\,</math>, and likewise <math>1-x = q_2\,</math>.
Doing comparative statics on the demand we find:
*Demand is less sensitive to the price differential as <math>t \,</math> (transport cost) increases
*Equal prices gives the firm captive demand plus half of intermediate segment <math>\frac{(1-b-a)}{2}\,</math>
*Taking <math>\frac{dq_1}{da}\,</math> shows that (for equal prices) getting closer steals demand: the '''demand effect'''
